Hi all,
I was working on a theoretical model about valuation distribution.
Assuming a Gamma distribution (or any other right skewed pdf).
I finally got a equation to solve for p:
1=p*f(p)/[1-F(p)]
where f(.|alpha, beta) is the pdf of the Gamma distribution, and F(.) is the
CDF.
alpha and beta are shape and scale parameters for Gamma.
I don't have to derive a closed form for p, but I need some properties of p
satisfying the equation.
Especially, I need the connection between this p and the solution, q, of
another equation with g and G substituting f and F. (if this is hard to get
in general,
how about g(.|a,b)=f(.|n*alpha,beta). (meaning g is only different from f
by
a parameter alpha, and g's alpha is n times of f's.
Thanks in advance.